Department of Mathematics
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Item New Dimensions in MCDM with Multi Phase Hyper Neutrosophic Sets(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Sunny Raza Qureshi; CIIT/FA19-RMT-025/LHR; Dr. Madiha Qayyum; LHR TP 7386This work introduces a new mathematical model of the human brain, the Multi-Phase Neutrosophic set, which is an extension of the Neutrosophic set: which deal with human mind uncertainties on a level-by-level basis, encountering sentimental and emotional activity in the human mind as well as presenting the mathematical expression of Neutrality - a distinct state of human psychology. Firstly, we have built a Neutrality degree for a Neutrosophic set and defined a new modified neutrosophic set called Neutro-intelligent set (NIS) which consist of membership, indeterminacy, neutrality and non-membership. We have built Neutro-Intelligent constructive and mathematical operators such as union, intersection, complement, cross product, and special product as well as two families of cardinality measure called Weighted Possible Cardinality and Weighted Neutral Cardinality. Using these measures we have defined relative sigma count and a Ranking Relation between Neutro-Intelligent Sets. Later, by utilizing the new introduced Neutrality Degree we have built a State/Phase Function –a function giving level wise classifications of human thought which then is employed in defining the initially mentioned Multi-Phase Neutrosophic set. A Neutro-Intelligent version of Multi- Phase Neutrosophic Set namely Final Phase Neutrosophic Set is also introduced in order to incorporate the basic building operations and measures in Multi-Phase Neutrosophic Set Theory and Logic. Moreover, we have worked on implementing a Multi-Phase Neutrosophic set in the MCDM environment, with a specific focus on developing an effective COVID -19 Medical Diagnosis approach.Item Ranking of Fuzzy Numbers and their Extension via Measures with Applications(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Sana Hayat; SP22-RMT-021; Dr. Madiha Qayyum; LHR TP 8727This study introduces advanced ranking techniques for extended fuzzy numbers, specifically in both an intuitionistic fuzzy environment and a neutrosophic environment. In the intuitionistic fuzzy setting, a novel ranking method is proposed using a similarity measure based on intuitionistic fuzzy bi-implicators. This approach is applied to rank extended fuzzy numbers and is further employed in the context of multicriteria decision-making problems. Additionally, in the neutrosophic environment, the work presents an artificial intelligence-based ranking methodology for extended fuzzy numbers (neutrosophic environment), utilizing cardinality-based similarity measures. This method involved the development of structures for Jaccard, Dice, and Sokal-Sneath-2 similarity measures. The research demonstrates the consistent ranking results across these measures for Single-Valued Neutrosophic Numbers (SVNNs), emphasizing the broad applicability of the proposed approach. The method's flexibility is highlighted by the incorporation of three distinct human mind states (optimistic, pessimistic, and neutral) through logical operators.